Answer :
Let's solve the problem by dividing each term of the polynomial [tex]\(42x^3 - 21x^2 + 49x\)[/tex] by [tex]\(7x\)[/tex].
1. Divide the first term:
[tex]\[
\frac{42x^3}{7x} = \frac{42}{7} \cdot \frac{x^3}{x} = 6x^2
\][/tex]
2. Divide the second term:
[tex]\[
\frac{21x^2}{7x} = \frac{21}{7} \cdot \frac{x^2}{x} = 3x
\][/tex]
3. Divide the third term:
[tex]\[
\frac{49x}{7x} = \frac{49}{7} \cdot \frac{x}{x} = 7
\][/tex]
Putting it all together, the expression [tex]\(42x^3 - 21x^2 + 49x\)[/tex] divided by [tex]\(7x\)[/tex] becomes:
[tex]\[
6x^2 - 3x + 7
\][/tex]
Therefore, the correct answer is:
[tex]\[6x^2 - 3x + 7\][/tex]
This corresponds to the option: [tex]\(6x^2 - 3x + 7\)[/tex].
1. Divide the first term:
[tex]\[
\frac{42x^3}{7x} = \frac{42}{7} \cdot \frac{x^3}{x} = 6x^2
\][/tex]
2. Divide the second term:
[tex]\[
\frac{21x^2}{7x} = \frac{21}{7} \cdot \frac{x^2}{x} = 3x
\][/tex]
3. Divide the third term:
[tex]\[
\frac{49x}{7x} = \frac{49}{7} \cdot \frac{x}{x} = 7
\][/tex]
Putting it all together, the expression [tex]\(42x^3 - 21x^2 + 49x\)[/tex] divided by [tex]\(7x\)[/tex] becomes:
[tex]\[
6x^2 - 3x + 7
\][/tex]
Therefore, the correct answer is:
[tex]\[6x^2 - 3x + 7\][/tex]
This corresponds to the option: [tex]\(6x^2 - 3x + 7\)[/tex].
